The Well-Posedness of Solutions for a Generalized Shallow Water Wave Equation

Shaoyong Lai and Aiyin Wang

Abstract and Applied Analysis, 2012, vol. 2012, 1-15

Abstract:

A nonlinear partial differential equation containing the famous Camassa-Holm and Degasperis-Procesi equations as special cases is investigated. The Kato theorem for abstract differential equations is applied to establish the local well-posedness of solutions for the equation in the Sobolev space with . Although the -norm of the solutions to the nonlinear model does not remain constant, the existence of its weak solutions in the lower-order Sobolev space with is proved under the assumptions and .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:872187

DOI: 10.1155/2012/872187

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